Recently, I found a wonderful OpenType font for Ancient Greek called Alexander (it comes with a nice italic Latin script too) – unlike other Greek fonts which I use & like (such as GFS Porson), this one comes with Ligatures! (Oh the excitement).
Unfortunately, I could not figure out how to get the Ligatures to be used in a multi-lingual document — if I just did \setmainfont[Ligatures={Rare,Historical}]{Alexander} it would work, but if I used the Polyglossia package and defined \newfontfamily\greekfont[Ligatures={Rare,Historical}]{Alexander} then the ligatures would not come up inside blocks of \textgreek{}. Hmmm. After much searching, I found out that you have to put Language=Greek and Script=Greek inside the options block of the font.
A nice long example would be done thus:
\usepackage{polyglossia,fontspec}
\setmainlanguage{english}
\setotherlanguages{ancientgreek}
\newfontfamily\greekfont[Ligatures={Rare,Historical},Script=Greek,Language=Greek]{Alexander}
\begin{document}
Some English text goes here (in the default font, normally "Latin Modern").
\textgreek{τῆς Τυνδαρ θυγατρὸς} -- some text in the Greek script
font that you defined with \newfontfamily\greekfont
-- now with ligatures! Great!
However, I recommend that you turn off the “Historical” ligatures option, unless you’re a bit manic — it has a rather weird omicron-upsilon ligature that modern eyes would not immediately read as such.